SChand Composite Mathematics Class 7 Chapter 15 Data Handling Exercise 15C

  Exercise 15 C

Question 1

Determine the mode for each of the following sets of data : 

(a) 5,3,5,2,3,5,1,7 

Ans: Mode 5

(b) 1,7,13,19,25

Ans: No mode 

(c) 4,6,8,4,10,4,6,12,6,10

Ans: 4 and 6 

(d) 51,68,70,76,76,55,70,73,68,70,81

Ans: 70

(e) 8,4,8,4,8,4,8,4,8,4,8,4

Ans: 4 and 8 

(f) 29,29,10,10,3,3,14,10,2,2

Ans: 10 

(g) 26,32,26,21,83,26,83,85

Ans: 26 and 83

Question 2

Find the mode of the following distributions: 

(a) 

$\begin{array}{|l|l|l|l|l|l|l|}\hline \text { Size } & 2 & 3 & 4 & 5 & 6 & 7 \\\hline \text { fre } & 4 & 6 & 2 & 5 & 3 & 1 \\\hline\end{array}$

Ans: Mode :3

(b) 

$\begin{array}{|l|l|l|l|l|l|}\hline \begin{array}{l}\text { Size of } \\\text { shoes }\end{array} & 6 & 7 & 8 & 9 & 10 \\\hline \begin{array}{l}\text { No of } \\\text { person }\end{array} & 12 & 20 & 40 & 15 & 7 \\\hline\end{array}$

Ans: Mode : 8 

Question 3

Determine (a) the mode (b) the median , and (c) the mean for each of the following sets of data: 

(i) $1,16,11,6,11,8,14,11,21$

Sol: mode = 11

1,6,8,11,11,14,16,21 

Median= 11

Mean $\bar{x}=\frac{Sum of observation}{No of observation}$

$=\frac{1+6+8+11+11+11+14+16+21}{9}$= $\frac{99}{9}=11$

(ii) $3,10,10,12,14,16,16,18,18,25$

Mode = 10,16 and 18 

Sol: 3,10,10,12,14,16,18,18,25 

Median = $\frac{14+16}{2}$

=$\frac{30}{2}=15$

Mean $\bar{x}=\frac{3+10+10+12+14+16+16+18+18+25}{10}$

=$\frac{142}{10}$ = 14.2

(iii) $23,2,42,6,36,11,29,9,15$

Mode = No mode

2,6,9,11,15,23,29,36,42

Median = 15

Mean

 $\begin{aligned} \bar{x} &=\frac{2+6,+9+11+15+23+29+36+42}{9} \\ &=\frac{173}{9}=19 \frac{2}{9} \end{aligned}$

(iv) $8,8,8,8,18,18,18,18$

Sol: Mode = 8 and 18 

8,8,8,8,18,18,18,18

Median = $\frac{8+18}{2}$

$=\frac{26}{2}=13$

$\operatorname{mean} \vec{x} =\frac{8,8,8,8,18,18,18,18}{8}$

$=\frac{104}{8}=13$

Question 4

Find the mode, and the mean for the set of data below.

Number of fiction books read by 28 eight grade pupils: 

$4,6,1,7,3,9,5,7,8,5,4,6,10,6,9,5,6,6,8,6,8,5,10,7,2,5,3,7$.

Sol: Mode = 6

Mean = $=\frac{4+6+1+7+3+9+5+7+8+5+4+6+10+6+9+5+6+6+8+6+8+5+10+7+2+5+3+7}{28}$

$=\frac{168}{28}$ = 6

Question 5

Find the mode and the mean of the following set showing number of hours of operating life of 25 flashlight batteries: 

$20,21,19,22,18,23,25,22,23,20,23,20,22,21,24,21,22,23,19,21,22,22,24,26,22 .$

Sol: Mode = 22 

Mean = $\frac{545}{25}=21.8$

Question 6

Tell whether the statement is true or false: 

(i) The mode is always one of the numbers in a data.- True 

(ii) The mean is one of the numbers in a data - False 

(iii) The median is always one of the numbers in a data- False